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  • 1.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, KTH Royal Inst Technol, NORDITA, Stockholm, Sweden..
    Magnetic helicity and fluxes in an inhomogeneous alpha(2) dynamo2018In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 339, no 9-10, p. 631-640Article in journal (Refereed)
    Abstract [en]

    Much work on turbulent three-dimensional dynamos has been done using triply periodic domains, in which there are no magnetic helicity fluxes. Here, we present simulations where the turbulent intensity is still nearly homogeneous, but now there is a perfect conductor boundary condition on one end and a vertical field or pseudovacuum conditions on the other. This leads to migratory dynamo waves. Good agreement with a corresponding analytically solvable alpha(2) dynamo is found. Magnetic helicity fluxes are studied in both types of models. It is found that at moderate magnetic Reynolds numbers, most of the magnetic helicity losses occur on large scales. Whether this changes at even larger magnetic Reynolds numbers, as required for alleviating the catastrophic dynamo quenching problem, remains stillunclear.

  • 2.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Univ Colorado, Lab Atmospher & Space Phys, Boulder, CO 80309 USA.;Univ Colorado, JILA, Boulder, CO 80309 USA.;Univ Colorado, Dept Astrophys & Planetary Sci, Boulder, CO 80309 USA.; Stockholm Univ, S-10691 Stockholm, Sweden.;Stockholm Univ, Dept Astron, Stockholm, Sweden..
    Chatterjee, Piyali
    Indian Inst Astrophys, Bengaluru, India..
    Strong nonlocality variations in a spherical mean-field dynamo2018In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 339, no 2-3, p. 118-126Article in journal (Refereed)
    Abstract [en]

    To explain the large-scale magnetic field of the sun and other bodies, the mean-field dynamo theory is commonly applied, where one solves the averaged equations for the mean magnetic field. However, the standard approach breaks down when the scale of the turbulent eddies becomes comparable to the scale of the variations of the mean magnetic field. Models showing sharp magnetic field structures have therefore been regarded as unreliable. Our aim is to look for new effects that occur when we relax the restrictions of the standard approach, which becomes particularly important at the bottom of the convection zone where the size of the turbulent eddies is comparable to the depth of the convection zone itself. We approximate the underlying integro-differential equation using a partial differential equation corresponding to a reaction-diffusion-type equation for the mean electromotive force, making an approach that is nonlocal in space and time feasible under conditions where spherical geometry and nonlinearity are included. In agreement with earlier findings, spatiotemporal nonlocality lowers the excitation conditions of the dynamo. Sharp structures are now found to be absent. However, in the surface layers, the field remains similar to before.

  • 3.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Hubbard, Alexander
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Käpylä, Petri
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Dynamical quenching with non-local alpha and downward pumping2015In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 336, no 1, p. 91-96Article in journal (Refereed)
    Abstract [en]

    In light of new results, the one-dimensional mean-field dynamo model of Brandenburg & Kapyla (2007) with dynamical quenching and a nonlocal Babcock-Leighton a effect is re-examined for the solar dynamo. We extend the one-dimensional model to include the effects of turbulent downward pumping (Kitchatinov & Olemskoy 2011), and to combine dynamical quenching with shear. We use both the conventional dynamical quenching model of Kleeorin & Ruzmaikin (1982) and the alternate one of Hubbard & Brandenburg (2011), and confirm that with varying levels of non-locality in the a effect, and possibly shear as well, the saturation field strength can be independent of the magnetic Reynolds number.

  • 4.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Oughton, S.
    Univ Waikato, Dept Math & Stat, Hamilton, New Zealand..
    Cross-helically forced and decaying hydromagnetic turbulence2018In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 339, no 9-10, p. 641-646Article in journal (Refereed)
    Abstract [en]

    We study the evolution of kinetic and magnetic energy spectra in magnetohydrodynamic flows in the presence of strong cross helicity. For forced turbulence, we find a weak inverse transfer of kinetic energy toward the smallest wavenumber. This is plausibly explained by the finiteness of scale separation between the injection wavenumber and the smallest wavenumber of the domain, which here is a factor of 15. In the decaying case, there is a slight increase at the smallest wavenumber, which is probably explained by the dominance of kinetic energy over magnetic energy at the smallest wavenumbers. Within a range of wavenumbers covering almost an order of magnitude, the decay is purely exponential, which is argued to be a consequence of a suppression of nonlinearity due to the presence of strong cross helicity.

  • 5.
    Brandenburg, Axel
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado; JILA and Department of Astrophysical and Planetary Sciences, University of Colorado, Boulder, Colorado; Department of Astronomy, AlbaNova University Center, Stockholm University, Stockholm, Sweden.
    Schober, J.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, I.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Laboratory for Atmospheric and Space Physics, University of Colorado, Boulder, Colorado; Department of Mechanical Engineering, Ben-Gurion University of the Negev, Beer-Sheva, Israel.
    The contribution of kinetic helicity to turbulent magnetic diffusivity2017In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 338, no 7, p. 790-793Article in journal (Refereed)
    Abstract [en]

    Using numerical simulations of forced turbulence, we show that for magnetic Reynolds numbers larger than unity, that is, beyond the regime of quasilinear theory, the turbulent magnetic diffusivity attains an additional negative contribution that is quadratic in the kinetic helicity. In particular, for large magnetic Reynolds numbers, the turbulent magnetic diffusivity without helicity is about twice the value with helicity. Such a contribution was not previously anticipated, but, as we discuss, it turns out to be important when accurate estimates of the turbulent magnetic diffusivity are needed.

  • 6.
    Kapyla, P. J.
    et al.
    Leibniz Inst Astrophys Potsdam, Sternwarte 16, D-11482 Potsdam, Germany.;Aalto Univ, Dept Comp Sci, ReSoLVE Ctr Excellence, Aalto, Finland.;Max Planck Inst Sonnensyst Forsch, Gottingen, Germany..
    Kapyla, M. J.
    Aalto Univ, Dept Comp Sci, ReSoLVE Ctr Excellence, Aalto, Finland.;Max Planck Inst Sonnensyst Forsch, Gottingen, Germany..
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA. Stockholm Univ, Stockholm, Sweden.;Stockholm Univ, AlbaNova Univ Ctr, Dept Astron, Stockholm, Sweden.;Univ Colorado, JILA, Boulder, CO 80309 USA.;Univ Colorado, Dept Astrophys & Planetary Sci, Boulder, CO 80309 USA.;Lab Atmospher & Space Phys, Boulder, CO USA..
    Small-scale dynamos in simulations of stratified turbulent convection2018In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 339, no 2-3, p. 127-133Article in journal (Refereed)
    Abstract [en]

    Small-scale dynamo action is often held responsible for the generation of quiet Sun magnetic fields. We aim to determine the excitation conditions and saturation level of small-scale dynamos in nonrotating turbulent convection at low magnetic Prandtl numbers. We use high-resolution direct numerical simulations of weakly stratified turbulent convection. We find that the critical magnetic Reynolds number for dynamo excitation increases as the magnetic Prandtl number is decreased, which might suggest that small-scale dynamo action is not automatically evident in bodies with small magnetic Prandtl numbers, such as the Sun. As a function of the magnetic Reynolds number (Rm), the growth rate of the dynamo is consistent with an Rm(1/2) scaling. No evidence for a logarithmic increase of the growth rate with Rm is found.

  • 7.
    Kemel, Koen
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Kleeorin, Nathan
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Rogachevskii, Igor
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Properties of the negative effective magnetic pressure instability2012In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 333, no 2, p. 95-100Article in journal (Refereed)
    Abstract [en]

    As was demonstrated in earlier studies, turbulence can result in a negative contribution to the effective mean magnetic pressure, which, in turn, can cause a large-scale instability. In this study, hydromagnetic mean-field modelling is performed for an isothermally stratified layer in the presence of a horizontal magnetic field. The negative effective magnetic pressure instability (NEMPI) is comprehensively investigated. It is shown that, if the effect of turbulence on the mean magnetic tension force vanishes, which is consistent with results from direct numerical simulations of forced turbulence, the fastest growing eigenmodes of NEMPI are two-dimensional. The growth rate is found to depend on a parameter beta(star) characterizing the turbulent contribution of the effective mean magnetic pressure for moderately strong mean magnetic fields. A fit formula is proposed that gives the growth rate as a function of turbulent kinematic viscosity, turbulent magnetic diffusivity, the density scale height, and the parameter beta(star). The strength of the imposed magnetic field does not explicitly enter provided the location of the vertical boundaries are chosen such that the maximum of the eigenmode of NEMPI fits into the domain. The formation of sunspots and solar active regions is discussed as possible applications of NEMPI.

  • 8.
    Käpylä, Petri J.
    et al.
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Mantere, Marit
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Brandenburg, Axel
    KTH, Centres, Nordic Institute for Theoretical Physics NORDITA.
    Effects of stratification in spherical shell convection2011In: Astronomical Notes - Astronomische Nachrichten, ISSN 0004-6337, E-ISSN 1521-3994, Vol. 332, no 9-10, p. 883-890Article in journal (Refereed)
    Abstract [en]

    We report on simulations of mildly turbulent convection in spherical wedge geometry with varying density stratification. We vary the density contrast within the convection zone by a factor of 20 and study the influence of rotation on the solutions. We demonstrate that the size of convective cells decreases and the anisotropy of turbulence increases as the stratification is increased. Differential rotation is found to change from anti-solar (slow equator) to solar-like (fast equator) at roughly the same Coriolis number for all stratifications. The largest stratification runs, however, are sensitive to changes of the Reynolds number. Evidence for a near-surface shear layer is found in runs with strong stratification and large Reynolds numbers.

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